I don't think this has been mentioned, but it kind of depends on where your multiple laptops / desktops are. Is this always on your own home network? Because in that case you don't even need a remote service like Github

If so, you can create a network drive on any of the devices - mount the network device on your other devices, and then create a local git repo there. Just remember that using an external git service is also a backup. So if you do everything locally, make sure to have your own backups in place

A much, much worse but also possible solution is to just put your projects into onedrive/dropbox/gdrive and sync it everywhere. It works for syncing, since you're saying that's the main objective - but you lose out on version control